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Search: id:A117152
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| A117152 |
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Sum of product of Fibonacci and triangular numbers. |
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+0
1
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| 0, 0, 1, 7, 25, 75, 195, 468, 1056, 2280, 4755, 9650, 19154, 37328, 71635, 135685, 254125, 471317, 866669, 1581620, 2866970, 5165630, 9256871, 16507092, 29304660, 51812160, 91264885, 160207603, 280340161, 489117135, 851054535
(list; graph; listen)
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OFFSET
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0,4
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REFERENCES
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A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003
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FORMULA
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a(n) = sum C(k,2)*F(k), k=2 to n, where F(n) = A000045(n), the Fibonacci numbers, and C(n, 2) = A000217(n-1), the triangular numbers, n(n-1)/2.
a(n) = C(n,2) F(n+2) - n F(n+3) + F(n+5) - 5
ogf = x^2(1 + 3x + x^3)/((1 - x)(1 - x - x^2)^3)
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MATHEMATICA
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Binomial[n, 2]Fibonacci[n + 2] - n Fibonacci[n + 3] + Fibonacci[n + 5] - 5
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CROSSREFS
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Cf. A086926, A014286.
Sequence in context: A001296 A000970 A048477 this_sequence A058481 A138729 A035509
Adjacent sequences: A117149 A117150 A117151 this_sequence A117153 A117154 A117155
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KEYWORD
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nonn,easy
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AUTHOR
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Mitch Harris (harris.mitchell(AT)mgh.harvard.edu), Feb 28, 2006
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